Help-Verizon Samsung Galaxy Note 3 with Straight Talk

I recently purchased a Verizon Samsung Galaxy Note 3, a CDMA phone with a SIM card.
I need some technical help with it.

I activated it with Straight Talk a week or so go and their BYOP activation kit made me activate it using a GSM/unlocked SIM. SO, now I have a Verizon Galaxy Note 3 , that runs off ATT network. AT&T coverage is terrible in our area. I purchased the phone as a Verizon phone so it would use Verizon’s network. Any idea how I get the phone to work for straight talk, but use Verizon network..

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As far as I know Straight Talk no longer uses Verizon's network or only does in certain markets with certain phones.